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  <div class="section" id="numpy-random-dirichlet">
<h1>numpy.random.dirichlet<a class="headerlink" href="#numpy-random-dirichlet" title="Permalink to this headline">¶</a></h1>
<dl class="function">
<dt id="numpy.random.dirichlet">
<code class="sig-prename descclassname">numpy.random.</code><code class="sig-name descname">dirichlet</code><span class="sig-paren">(</span><em class="sig-param">alpha</em>, <em class="sig-param">size=None</em><span class="sig-paren">)</span><a class="headerlink" href="#numpy.random.dirichlet" title="Permalink to this definition">¶</a></dt>
<dd><p>Draw samples from the Dirichlet distribution.</p>
<p>Draw <em class="xref py py-obj">size</em> samples of dimension k from a Dirichlet distribution. A
Dirichlet-distributed random variable can be seen as a multivariate
generalization of a Beta distribution. The Dirichlet distribution
is a conjugate prior of a multinomial distribution in Bayesian
inference.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>New code should use the <code class="docutils literal notranslate"><span class="pre">dirichlet</span></code> method of a <code class="docutils literal notranslate"><span class="pre">default_rng()</span></code>
instance instead; see <em class="xref py py-obj">random-quick-start</em>.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>alpha</strong><span class="classifier">array</span></dt><dd><p>Parameter of the distribution (k dimension for sample of
dimension k).</p>
</dd>
<dt><strong>size</strong><span class="classifier">int or tuple of ints, optional</span></dt><dd><p>Output shape.  If the given shape is, e.g., <code class="docutils literal notranslate"><span class="pre">(m,</span> <span class="pre">n,</span> <span class="pre">k)</span></code>, then
<code class="docutils literal notranslate"><span class="pre">m</span> <span class="pre">*</span> <span class="pre">n</span> <span class="pre">*</span> <span class="pre">k</span></code> samples are drawn.  Default is None, in which case a
single value is returned.</p>
</dd>
</dl>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><dl class="simple">
<dt><strong>samples</strong><span class="classifier">ndarray,</span></dt><dd><p>The drawn samples, of shape (size, alpha.ndim).</p>
</dd>
</dl>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><dl class="simple">
<dt><strong>ValueError</strong></dt><dd><p>If any value in alpha is less than or equal to zero</p>
</dd>
</dl>
</dd>
</dl>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="numpy.random.Generator.dirichlet.html#numpy.random.Generator.dirichlet" title="numpy.random.Generator.dirichlet"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Generator.dirichlet</span></code></a></dt><dd><p>which should be used for new code.</p>
</dd>
</dl>
</div>
<p class="rubric">Notes</p>
<p>The Dirichlet distribution is a distribution over vectors
<img class="math" src="../../../_images/math/888f7c323ac0341871e867220ae2d76467d74d6e.svg" alt="x"/> that fulfil the conditions <img class="math" src="../../../_images/math/56aab1ca3a770b05210a22a2867227a77b70b5d3.svg" alt="x_i&gt;0"/> and
<img class="math" src="../../../_images/math/5389acfbfe13838d682262b93d1553c41213dda5.svg" alt="\sum_{i=1}^k x_i = 1"/>.</p>
<p>The probability density function <img class="math" src="../../../_images/math/141bbefb74014fc5e43499901bf78607ae335583.svg" alt="p"/> of a
Dirichlet-distributed random vector <img class="math" src="../../../_images/math/ed38fa24f1c94891bd312012aab3f6673be3eb83.svg" alt="X"/> is
proportional to</p>
<div class="math">
<p><img src="../../../_images/math/b6be0ea65ed0701a0c450cbfd66656df95d18bb6.svg" alt="p(x) \propto \prod_{i=1}^{k}{x^{\alpha_i-1}_i},"/></p>
</div><p>where <img class="math" src="../../../_images/math/2f5aa019312e1bbc969deab8dca8b00f76025404.svg" alt="\alpha"/> is a vector containing the positive
concentration parameters.</p>
<p>The method uses the following property for computation: let <img class="math" src="../../../_images/math/7daf0d4815e763eb90f0d5f1dc406f668c1e21db.svg" alt="Y"/>
be a random vector which has components that follow a standard gamma
distribution, then <img class="math" src="../../../_images/math/50609be1cfa120a6abb1cb4d65261376a93eb4d0.svg" alt="X = \frac{1}{\sum_{i=1}^k{Y_i}} Y"/>
is Dirichlet-distributed</p>
<p class="rubric">References</p>
<dl class="citation">
<dt class="label" id="r15565755312f-1"><span class="brackets">1</span></dt>
<dd><p>David McKay, “Information Theory, Inference and Learning
Algorithms,” chapter 23,
<a class="reference external" href="http://www.inference.org.uk/mackay/itila/">http://www.inference.org.uk/mackay/itila/</a></p>
</dd>
<dt class="label" id="r15565755312f-2"><span class="brackets">2</span></dt>
<dd><p>Wikipedia, “Dirichlet distribution”,
<a class="reference external" href="https://en.wikipedia.org/wiki/Dirichlet_distribution">https://en.wikipedia.org/wiki/Dirichlet_distribution</a></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<p>Taking an example cited in Wikipedia, this distribution can be used if
one wanted to cut strings (each of initial length 1.0) into K pieces
with different lengths, where each piece had, on average, a designated
average length, but allowing some variation in the relative sizes of
the pieces.</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">dirichlet</span><span class="p">((</span><span class="mi">10</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span> <span class="mi">20</span><span class="p">)</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">),</span> <span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">),</span> <span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">left</span><span class="o">=</span><span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;g&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">barh</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">),</span> <span class="n">s</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">left</span><span class="o">=</span><span class="n">s</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="n">s</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">color</span><span class="o">=</span><span class="s1">&#39;r&#39;</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Lengths of Strings&quot;</span><span class="p">)</span>
</pre></div>
</div>
<div class="figure align-default">
<img alt="../../../_images/numpy-random-dirichlet-1.png" src="../../../_images/numpy-random-dirichlet-1.png" />
</div>
</dd></dl>

</div>


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